An algorithm has been developed for the forced convective diffusion-reaction problem for convection inside and outside a droplet by a recirculating flow field hydrodynamically coupled at the droplet interface with an external flow field that at infinity becomes a uniform streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet or reactions can take place in both phases. The algorithm has been implemented and results are shown here for the case of no reaction and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.